Thermal diffusivity, is a material property and relates to the transient heat transfer speed through the particular material. This property is dependent on the heat transfer direction for anisotropic materials. Anisotropic materials are materials that have different properties along lines of different directions. For planar samples, the normal thermal diffusivity is a property of the speed at which heat is transferred through the thickness of the sample from the side where the heat is applied to the side where heat was not applied. Lateral thermal diffusivity is a property of the speed at which heat is transferred in a perpendicular direction within the material relative to the direction from which the heat has been applied.
An infrared thermal imaging system is used to determine values for normal and lateral thermal diffusivity of a material sample. Thermal imaging systems typically consist of an infrared camera, a personal computer (PC) equipped with a digital frame grabber and data acquisition and processing software, a flash lamp as a heat source, and electronics to monitor and control the system operation. Using this equipment, a flash thermal imaging test is performed. During the test, pulsed heat energy is applied to the sample""s back surface that has been partially shielded to prevent a portion of the material sample from being heated directly when the pulsed heat energy is applied. The change in temperature distribution on the opposite, front, surface is monitored by the infrared camera with a series of thermal images being captured and recorded within the PC.
The temperature distribution represents the effects of both the normal heat transfer through the thickness of the sample and the lateral heat transfer through the interface between the shielded and unshielded back-surface regions. The temperature distributions that are detected and recorded by the infrared camera are fitted with a theoretical solution of the heat transfer process to determine the lateral thermal diffusivity at the interface.
Zhong Ouyang, et. al. have published a method for measuring the lateral thermal diffusivity. Their theory was based on samples being infinite-sized plates, and required the manual fitting of the experimental data with the theoretical solution in spatial domain for single curves. Their theory also required the interface location to be pre-measured by hand and required even (uniform) heating. A solution for semi-infinite width (0 less than xc3x97 less than ∞) sample was used by Ouyang et al. (1998), as:             T      ⁢              (                  x          ,          L          ,          t                )              =                  1                  2          ⁢          L                    ⁢                        (                                    erfc              ⁢                              xe2x80x83                            ⁢                                                a                  -                  x                                                  2                  ⁢                                                                                    α                        x                                            ⁢                      t                                                                                            +                          erfc              ⁢                              xe2x80x83                            ⁢                                                a                  +                  x                                                  2                  ⁢                                                                                    α                        x                                            ⁢                      t                                                                                                    )                ⁡                  [                      1            +                          2              ⁢                                                ∑                                      n                    =                    1                                    ∞                                ⁢                                                                            (                                              -                        1                                            )                                        n                                    ⁢                                      exp                    ⁢                                          (                                                                        -                                                                                                                    n                                2                                                            ⁢                                                              π                                2                                                                                                                    L                              2                                                                                                      ⁢                                                  α                          z                                                ⁢                        t                                            )                                                                                                    ]                      ,
where T is temperature; x is a point along an x-axis; L is sample thickness; t is time; a is the interface location along the x-axis; xcex1x, and xcex1z are the lateral (along the x-axis) and through-thickness (along the z-axis) thermal diffusivities, respectively; and n corresponds to the number of terms used in the summation.
The present system and method for determining normal and lateral thermal diffusivity uses finite boundaries to determine the diffusivity. Ouyang""s method simplifies the determination by using semi-infinite boundaries. The present system takes non-uniform heating into consideration by explicitly calculating the temperature amplitude at each pixel. The present system may also be used as a nondestructive method to detect and locate material defects within the sample (cracks perpendicular to the sample surface). The depth of a crack within the material can be determined by the defect""s correlating diffusivity value. Existing nondestructive techniques for detecting material defects include ultrasound technology. However, ultrasound techniques are time consuming for detecting this type of defect in large material samples.
Transient thermography has been used for the nondestructive detection of material flaws (see U.S. Pat. No. 5,711,603, Ringermacher et al. (xe2x80x9c""603xe2x80x9d). The ""603 patent describes a method for flaw depth detection using thermal imaging captured by an infrared camera. The thermal imaging technique used in the ""603 patent applies pulsed thermal energy to the sample surface and subsequently a thin layer of material on the surface will be instantaneously heated to a high temperature. Heat transfer takes place from the surface that was heated to the interior of the sample resulting in a continuous decrease of the surface temperature. If a plain crack (a crack with a plane parallel to the sample surface that was heated) exists, the heat is restricted from further transfer deeper into the sample material. Therefore, the surface temperature at this region will remain higher than in surrounding areas so that the sample material above the plain crack will be viewed as a xe2x80x9chot spotxe2x80x9d by the infrared receptors. The hot spot will occur earlier during the analysis if the crack is shallow and will appear later in the analysis if the crack is deeper. In ""603 a correlation was developed between the measured time when the highest hot spot contrast occurs and relative depth of the crack within the sample. The analysis was performed pixel by pixel and the final relative depth for all pixels is composed into an image (or map). The relative depth is color coded and presented as the result.
Differences between the xe2x80x2603 patent and the present system include the type of crack or defect that may be detected. The ""603 patent detects plain cracks that are completely within the material and are oriented parallel to the heated sample surface (like an air gap or delamination defect). The present invention detects cracks that are perpendicular to the heated surface and these cracks may be of varying depths that include surface cracks. The ""603 patent uses an empirical correlation between time of hot spot occurrence and crack depth. The present system fits experimental temporal-spatial curves with a theoretical model. The ""603 patent also derives an image of relative depth of defect from the surface while the present system derives the depth (or length) of the crack extending from the surface to the inside of the sample.
The object of this invention is to provide an automated and accurate method for determining the lateral thermal diffusivity of a material sample using a model that contains finite boundaries.
Another object of this invention is to provide a nondestructive method for the detection of cracks within a material sample by use of the method used to determine thermal diffusivity.
A system and method for determining lateral thermal diffusivity of a material sample using a heat pulse; a sample oriented within an orthogonal coordinate system; an infrared camera; and a computer that has a digital frame grabber, and data acquisition and processing software. The mathematical model used within the data processing software is capable of determining the thermal diffusivity of a sample of finite boundaries. The system and method may also be used as a nondestructive method for detecting and locating cracks within the material sample.